> [!theorem] Strategy > > Let $(L)$ be a [[First Order Inexact ODE|first order ODE]]. If it is quadratic (in the form of) > $ > \frac{dy}{dx} = f(Ax + By + C) > $ > Then substituting $u = Ax + By + C$ with > $ > \frac{du}{dx} = A + B\frac{dy}{dx} = A + Bf(u) > $ > gives a separable equation. $u$ would be an affine combination of $x$ and $y$.